Focus on Problem Solving

Boron is widely used in the production of enamels and glasses. Naturally occurring boron has an average atomic mass of 10.811 amu. If the only isotopes present are and B, describe how you would determine their relative abundances. Include in your description any information that you would need to look up. 

This problem is similar to those in the chapter for determining atomic masses. Those problems were cases where we had two unknowns and two equations. There seems to be too little information provided here for that approach, though, so we need to consider any additional relationships that are implied in the problem. If we can write an extra formula that relates the amount of B and B, that should provide the additional equation we need to solve this problem. We ll also need to know the mass of each isotope. 

Because we need to know the mass of each isotope to solve this problem, that information would have to be looked up. We could get a rough approximation by assuming that °B has a mass of 10 amu and B has a mass of 11 amu, but we probably need better data than that. The extra equation we need arises from the fact that we are told that only two isotopes exist. Thus the abundances of the two must add up to 100%. This gives us a first equation  

The fact that the resulting average atomic mass is 10.811 provides another equation  

Now we have two equations in two unknowns (assuming we have looked up the needed masses), so the problem can be solved. 

---

Problem Sets Each chapter includes roughly 100 problems and exercises, spanning a wide range of difficulty. Most of these exercises are identified with specific sections to provide the practice that students need to master material fi-om that section. Each chapter also includes a number of Additional Problems, which are not tied to any particular section and which may incorporate ideas fi-om multiple sections. Focus on Problem Solving exercises follow, as described earlier. The problems for most chapters conclude with Cumulative Problems, which ask students to synthesize information from the current chapter with what they ve learned fi-om previous chapters to form answers. Answers for all odd-numbered problems appear at the end of the book in Appendix K... 

---